Dairy cow dry matter intake for multiverse analysis and Bradley-Terry modeling

The palatability of feed for dairy cows is an important consideration but is difficult to measure, particularly when considering more than two feeds. We outline how a combination of multiverse analysis and Bradley-Terry modeling, two methodological tools that have rarely been applied in dairy science, can be adapted to address this problem. Specifically, we propose to apply multiverse analysis as a way to consider a range of thresholds for how much of a mixed grass-legume (MGL) silage had to be consumed (as a percent of the total DMI) to be designated as preferred. Each threshold gives rise to a separate dataset and a corresponding fitted Bradley-Terry model. Bradley-Terry models attribute to each feed what is commonly referred to as an "ability" in the context of sports or other competitions but can be interpreted as palatability when applied to feeds. This combined approach is a way of estimating palatabilities that appropriately reflect the degree of preference cows express through their feeding behavior. It has the advantages of being transparent and relatively easy to implement. A possible disadvantage is that this method is limited to a paired comparison approach and has difficulties with main-effects statistical inference. We demonstrate the use of this methodology on an example dataset comparing MGL silages under different ensiling conditions and exposed to oxygen for different durations.